Question

You are given the rate equation −r_A" = -k_A" C_A for the liquid-phase reaction A--->B. Inlet flow rates are 100 mol/s of pure A, which has a density of 1000 kg/m3 and a molar mass 1000 g/mol. The rate constant is 1x10^-6m/s. You are told the reactor has a catalyst of surface area S_g of 5 m²/g, and the catalyst density in the reactor  is 25 kg/m³.

a.  To achieve 50% conversion in an isothermal steady-state CSTR, what is the volume required?

b.  What volume is required for the same conversion in an isothermal steady-state, PBR?

c.  What is the residence time in a CSTR vs a PBR?  Calculate a residence time with units of volumetric flowrate/catalyst weight as well as the usual volumetric flowrate/reactor volume. The former does not have the convenient units of time but physically expresses the residence time accurately in a reaction catalyzed by a solid catalyst in a reactor.  Explain physically in a single sentence why the residence time for the CSTR is different from the PBR.

d.  You decide to cut the residence time by ½ by doubling flow rates. What happens to the conversion in the PBR and CSTR above?

Answer 1

(1) For CSTR Mole balance reaction for A is

$V= \frac{F_{A_0}-F_A}{-r_A}= \frac{C_{A_0v_0}-C_Av_0}{kC_A}$

Where

V= reactor volume

FA0= Inlet flow rate

FA= outlet flow rate

rA= reaction rate

C_A0 = initial concentration

C_A= final concentration

v0= volumetric flow rate

k = rate constant

At 50% conversion

$K_A= 1\times 10^{-6} M^-s^-$
Inlet Flow rate
$C_{A_0 }= \frac{Density}{Molar \ mass}= \frac{1000\times 1000g/m^3}{1000g/mol}= 1000mol/m^3$

$\Rightarrow C_A = 0.5 C_{A_0}= 0.5 \times 1000 = 500 mol/m^3$

From the inlet flow rate formula calculate Volumetric flow rate

$\Rightarrow$ $v_0= \frac{F_{A_0}}{C_{A_0}}= \frac{100mol/s}{1000mol/m^3}= 0.1 m^3/s$

Now From the Mole balance formula for A=

$V= \frac{C_{A_0v_0}-C_Av_0}{kC_A}$

$V= \frac{(1000mol/m^3\times 0.1 m^3/s)-(500mol/m^3\times 0.1 m^3/s)}{(1\times 10^{-6}mol/s) \times (500mol/m^3)}$

therefore to achieve 50% conversion in an isothermal steady-state CSTR, the volume required is